Approximation and quick calculation: Evaluate 1010 ÷ 36 + (187 × 20.05) and select the closest option.

Introduction / Context:
Blend a small division with a product near a clean multiple. The product dominates the sum, so compute it accurately and add the modest quotient to pick the nearest option among values in the 3700–3800s.

Given Data / Assumptions:

• 1010 / 36 is roughly 28.06
• 187 * 20.05 ≈ 187*(20 + 0.05)

Concept / Approach:
Compute 187*20 quickly and add 187*0.05, then add the division result. Because options differ by tens, accuracy to within a few units is enough.

Step-by-Step Solution:

Verification / Alternative check:
Exact computation yields about 3777.41; among 3650, 3770, 3825, 3800, the nearest is 3770 (distance ~7.4).

Why Other Options Are Wrong:
3650 is too low; 3825 and 3800 are higher by 47–23 respectively; 3770 is closest.

Common Pitfalls:
Missing the 0.05 component (9.35), which would understate the sum and skew the choice downward.

Final Answer:
3770